Presently, multi-hop (or “decode-and-forward”) wireless transmission systems, e.g., adhering to the well-known IEEE 802.11 standard, often include “passive” relays in the paths between source terminals and destination terminals. The relays serve to increase the effective length of the paths within the transmission systems by retransmitting symbols received from the source terminals to the destination terminals.
Some relays, often referred to as sleep-listen-or-talk, or “SLoT,” relays, are unable to receive and retransmit simultaneously. Such relays are therefore unavailable to receive symbols while they are transmitting. SLoT relays and their corresponding destination terminals negotiate to determine the intervals during which they receive and also the intervals during which they transmit. Since the designation of an interval as a transmit interval or a receive interval is fixed ahead of time, such relays are said to be carrying out a fixed SLoT strategy. Unfortunately, fixed SLoT strategies are unable to achieve the capacity of a wireless relay channel.
It is known that multi-hopping, or decode-and-forward, achieves the capacity of wireless relay channels if the relay is near the source terminal and if the channel phase is “random” and known only locally (see, e.g., Kramer, et al., “Capacity Theorems for Wireless Relay Channels,” Proc. 41st Annu. Allerton Conf. on Communication, Control, and Computing, (Monticello, Ill.), pp. 1074-1083, Oct. 1-3, 2003). (“Random” as used in this art means chaotic and not necessarily mathematically random.)
This capacity result is also valid if the relay cannot transmit and receive at the same time, as long as the destination knows the source and relay operating modes, and the fraction of time the relay listens to the source is lower bounded by a positive number (see, e.g., Kramer, et al., “Cooperative Strategies and Capacity Theorems for Relay Networks,” IEEE Trans. Inform. Theory, submitted February 2004). The latter situation occurs, e.g., when protocols or energy constraints restrict the amount of time the relay can transmit.
Some information theory for relays that cannot receive and transmit simultaneously has already been developed (see, e.g., Gastpar, et al., “On the Capacity of Large Gaussian Relay Networks,” Proc. IEEE Infocom 2002, New York, June 2002; Høst-Madsen, “On the Capacity of Wireless Relaying,” Proc. IEEE Vehic. Techn. Conf, VTC 2002 Fall, (Vancouver, BC), vol. 3, pp. 1333-1337, Sep. 24-28, 2002; Khojastepour, et al., “On the Capacity of ‘Cheap’ Relay Networks,” Proc. 37th Annu. Conf. on Information Sciences and Systems (CISS), (Baltimore, Md.), Mar. 12-14, 2003; and Nabar, et al., “Capacity Scaling Laws in MIMO Wireless Networks,” Proc. 41st Annu. Allerton Conf. on Communication, Control, and Computing, (Monticello, Ill.), pp. 378-389, Oct. 1-3, 2003 and references therein). Unfortunately, all of the theory developed to date has assumed a fixed SLoT strategy, i.e., all terminals know at all times which mode (receive or transmit) every terminal is using.
What is needed in the art is an extension of information theory to relays and transmitters capable of carrying out a random SLoT strategy. What is further needed in the art is an extension of information theory to channels that are memoryless and with cost constraints. What is still further needed in the art is an extension of information theory to SLoT relays. Ultimately, what is needed in the art are relays and methods of operating a transmitter that increase channel utilization in both wireless and wireline communications networks.